## Calculus (3rd Edition)

Given $$\sum_{n=1}^{\infty} \frac{n}{\sqrt{n^2+1}}$$ Since \begin{align*} \lim _{n \rightarrow \infty} \frac{n}{\sqrt{n^2+1}}&=\lim _{n \rightarrow \infty} \frac{1}{\sqrt{1+1/n^2}}\\ &=1 \neq 0 \end{align*} Since the $n$th term $a_{n}$ does not converge to zero, thus the series diverges.